[seqfan] A permutation with chunks, sums and division

Eric Angelini Eric.Angelini at kntv.be
Fri Nov 28 17:11:56 CET 2014


Hello SeqFans,
S=1,2,4,3,5,6,7,8,9,15,10,11,12,13,14,16,17,18,19,20,22,21,23,24,25,26,27,a,...

Put a < : > immediately after the 1st integer, then (from there) another < : >
after 2 integers, then after 4 integers, then after 3 integers, etc. (those
marks are placed according to the sequence S itself):

S=1:2,4:3,5,6,7:8,9,15:10,11,12,13,14:16,17,18,19,20,22:21,23,24,25,26,27,a:...

We see now a succession of :chunks: -- where the sum of the integers in each
chunk is divisible by the first integer of the said chunk (T=sum; D=division):

S=1:2,4:3,5,6,7:8,9,15:10,11,12,13,14:16,17,18,19,20,22:21,23,24,25,26,27,a:...
T=1  6     21     32         60               122            146+a
D=  6/2   21/3   32/8       60/10            122/16        146+a /21

As S must always be extended with the smallest available integer not yet present
in S, we see (at the end of the present sequence) that the smallest available 
< a >, must be = 43.

S is the lexico-first permutation of the integers >0 with this property.

Best,
É.
 


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